Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation
[Espaces de modules de faisceaux semistables par rapport à une polarisation kählérienne]
Journal de l'École polytechnique — Mathématiques, Tome 7 (2020) , pp. 233-261.

En utilisant le critère d’existence d’un bon espace de modules d’un champ d’Artin dû à Alper–Fedorchuk–Smyth, nous construisons un espace de modules propre de faisceaux de rang 2 sur une variété projective complexe donnée, de classes de Chern fixées et qui sont Gieseker-Maruyama-semistables par rapport à une classe de Kähler fixée.

Using an existence criterion for good moduli spaces of Artin stacks by Alper–Fedorchuk–Smyth we construct a proper moduli space of rank two sheaves with fixed Chern classes on a given complex projective manifold that are Gieseker-Maruyama-semistable with respect to a fixed Kähler class.

Reçu le : 2018-08-15
Accepté le : 2019-11-25
Publié le : 2020-01-15
DOI : https://doi.org/10.5802/jep.116
Classification : 32G13,  14D20,  14D23,  14J60
Mots clés: Variétés de Kähler, modules de faisceaux cohérents, champs algébriques, bons espaces de modules, déformations semi-universelles, présentations quotient locales
@article{JEP_2020__7__233_0,
     author = {Daniel Greb and Matei Toma},
     title = {Moduli spaces of sheaves that are semistable with respect to a K\"ahler polarisation},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     publisher = {\'Ecole polytechnique},
     volume = {7},
     year = {2020},
     pages = {233-261},
     doi = {10.5802/jep.116},
     zbl = {07152736},
     language = {en},
     url = {jep.centre-mersenne.org/item/JEP_2020__7__233_0/}
}
Daniel Greb; Matei Toma. Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation. Journal de l'École polytechnique — Mathématiques, Tome 7 (2020) , pp. 233-261. doi : 10.5802/jep.116. https://jep.centre-mersenne.org/item/JEP_2020__7__233_0/

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